What is (7-4i)/(4+9i) ?

The solution to (7-4i)/(4+9i) is -8/97-79/97 i

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simplify (7-4i)/(4+9i)

simplify

\frac{7 - 4 i}{4 + 9 i}

- \frac{8}{97} - \frac{79}{97} i

Solution steps

\frac{7 - 4 i}{4 + 9 i}

Multiply by the conjugate

\frac{4 - 9 i}{4 - 9 i}

= \frac{( 7 - 4 i ) ( 4 - 9 i )}{( 4 + 9 i ) ( 4 - 9 i )}

Simplify

\frac{( 7 - 4 i ) ( 4 - 9 i )}{( 4 + 9 i ) ( 4 - 9 i )} : \frac{- 8 - 79 i}{97}

= \frac{- 8 - 79 i}{97}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 8}{97} + \frac{- 79}{97} i

Simplify

\frac{- 8}{97} + \frac{- 79}{97} i : - \frac{8}{97} - \frac{79}{97} i

= - \frac{8}{97} - \frac{79}{97} i

\frac{3}{8} \div \frac{13}{12}

- 7 (8 x - 3) + x

9 x^{2} y - 12 x y^{2}

(3 a)^{4}

2200 - 102